Remove dough from plastic bag, keeping the smooth top side facing up. Place it on a lightly floured work surface and lightly dust the dough with flour. Using your fingertips (but not your nails), press down on the dough to flatten it and push it outward into a larger circle. Flip the dough over and repeat on the other side, and then flip the dough back over. (You always want the smooth side up.)

Thinking of the circle of dough as a clock face, make a fist with your left hand and place it firmly at the 9 o'clock position, about one inch in from the edge (this will keep the edge of the dough slightly thicker). Place your right hand at the 3 o'clock position, putting your thumb on top of the dough and your other fingers underneath. Lift the dough and stretch it a bit. Move the dough a one-eighth turn and repeat. Continue until you have evenly stretched the dough into a 9-inch circle with slightly thicker edges.

Dust the pizza peel generously with flour. Using your hands and working quickly, lift and transfer the dough to the pizza peel. Give the peel a few shakes back and forth to make sure the dough is not sticking.

To top the pizza: Spread the pizza sauce evenly over the dough, leaving a 1-inch border. Distribute the slices of mozzarella evenly over the top. Distribute the tomato slices evenly over the cheese. Drizzle the olive oil over the tomatoes.

Give the peel another gentle shake back and forth just to make sure the dough is not sticking. Slide the dough from the peel onto the hot baking stone using a jerking motion with your arm. Work quickly to slide the pizza into the grill and close the top so the temperature doesn't drop too much. Bake the pizza until the crust is crisp and golden brown, about 8 minutes. Using the peel, remove the pizza from the grill and transfer to a cutting board. Scatter the basil leaves over the pizza. Slice the pizza into wedges and serve immediately.